Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with \((C,\alpha ,\rho ,d)\)-convexity
type: Item
instance of: scholarly article
title: Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with \((C,\alpha ,\rho ,d)\)-convexity
zbMATH Open document ID: 1229.90258
author: Juan-Miguel Gracia
published in: Journal of Optimization Theory and Applications
publication date: 2011-03-10T00:00:00Z
review text: The authors consider a class of nondifferentiable multi-objective fractional programming problems in which each component of the objective function contains a term involving the support function of a compact convex set. For the investigations in this paper, \((C, \alpha \rho, d)\)-convexity is assumed which has been recently introduced by \textit{D. H. Yuan, X. L. Liu, A. Chinchuluun} and \textit{P. M. Pardalos} [J. Optim. Theory Appl. 129, No. 1, 185--199 (2006; Zbl 1146.90077)]. Under this assumption, some sufficient optimality conditions (Section 3) and (weak and strong) duality results (Section 4) for weakly efficient solutions of such problems are derived. The results of this paper generalize previous results given by \textit{D. S. Kim, S. J. Kim} and \textit{M. H. Kim} [J. Optim. Theory Appl. 129, No. 1, 131--146 (2006; Zbl 1149.90135)] and \textit{X.-J. Long, N.-J. Huang} and \textit{Z.-B. Liu} [J. Ind. Manag. Optim. 4, No. 2, 287--298 (2008; Zbl 1161.90480)].
reviewed by: Frank Werner
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C32
zbMATH DE Number: 5864221
zbMATH Keywords: nondifferentiable multi-objective fractional programming
zbMATH Keywords: sufficient optimality condition
zbMATH Keywords: weak and strong duality
zbMATH Keywords: weakly efficient solution
zbMATH Keywords: \((C, \alpha, \rho,d)\)-convexity
MaRDI profile type: Publication
full work available at URL: s10957-010-9740-z
OpenAlex ID: W2062360657
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DOI: 10.1007/S10957-010-9740-Z
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description: scientific article; zbMATH DE number 5864221